(7 points) Suppose Backbeat BBQ, Dave Grohl's one-man catering company, offers two types of membershipplans. Plan A has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1per unit for using the service. Let x be expenditure on all other goods and y be the units of consumption ofBackbeat BBQ's services, and suppose you have an income of $100.A. Write down the budget equation that you would have after you paid the entry fee for each of the two plans.B. If your utility function is xy, how much y would you choose in each case?C. Which plan would you prefer? Explain.

Dear student, find a detailed answer and step by step solution in the explanation part…

Answered: (7 points) Suppose Backbeat BBQ, Dave…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose ABC Corp. spends $200,000 per year on some basic level of advertising, regardless of its revenues. In addition, the company spends 15 percent of each dollar of revenue on extra advertising. Write a mathematical equation that describes the functional relation between advertising (A) and revenue (R). A= (Enter your response as an expression.)
3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.
Assume the market clearing price is $5.00 for deli sandwiches and the amount of exchange that would take place at that price is 200 deli sandwiches per day. You, however, don't have this information and have just opened your deli. You decide to price your sandwiches at $9.00 and are willing and able to sell 285 sandwiches per day at that price. When you do this, you notice you sell 100 sandwiches per day. Draw this situation on a graph and then explain what will happen in this market -- i. e., if there is a shortage or surplus, show this on the graph and then explain what the shortage or surplus will cause to happen in the market. Make sure you talk about inventories in your answer.
3. A consumer's indirect utility function is given by V (p, y) = f(p)y. (a) What is the form of this consumer's expenditure function? (b) What kind of preferences does this consumer have?
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2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
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5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u4(x4) Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xg, q = 0, 1, 2, ...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. rA + 3r and uB(xB) 4x? + x. (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.
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Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a= b= (b₁,b₂) respectively. Solve for a and b. (a1, a2) and
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Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…

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